The present disclosure relates to control of the attitude or orientation of spacecraft, for example, to position a telescope mounted to a satellite to obtain an image of an object by reorienting the satellite itself. A typical spacecraft is equipped with a group or array of three or more control moment gyroscopes (CMGs) to facilitate attitude control of the vehicle. Spacecraft attitude control techniques commonly involve Eigen axis rotations. Eigen axis rotations are desirable as they are intuitively simple to construct and provide the advantage of reorienting the spacecraft along the shortest circular arc between the starting and desired final attitude angles. The angular error defined by translation from a first orientation to a second orientation can be represented as rotation through a certain angle about a particular fixed axis, referred to as the Eigen axis of the rotation. Once the Eigen axis has been determined, two other axes that need not be aligned with the reference spacecraft body fixed frame may be selected to form an orthogonal set with the Eigen axis. Since the entire rotation from the initial to the final states is performed about the Eigen axis, the other two axes will always have zero angles to be traversed. Eigen axis rotations are normally implemented as rest-to-rest maneuvers. That is, the rotation is initiated from rest and terminated when the spacecraft is again at rest in the new desired orientation. A maneuver similar to an Eigen axis rotation can be constructed when it is desired to initiate a reorientation maneuver from a non-resting state and/or when it is desired to terminate a reorientation maneuver at a non-resting state. For such non-rest maneuvers, rotations will normally be carried out as simultaneous rotations about three orthogonal axes and designed similarly to an Eigen axis maneuver according to the kinematic differential equations.
Many spacecraft systems are used in a manner that demands expeditious reorientation. For instance, it is important in many satellite missions to perform attitude maneuvers as rapidly as possible, where the capacity of commercial Earth observing satellites can be improved by maneuvering more quickly to reduce the time needed to slew between image regions. By reducing the slew time, it is possible for the satellite to acquire additional images and maximize revenue. Accordingly, time-optimal attitude maneuvers have been the subject of extensive study, and such time-optimal reorientation maneuvers were demonstrated in flight, for the first time, on board the NASA space telescope TRACE. The effectiveness of a CMG-based satellite may be improved by integrating time-optimal (shortest-time) attitude maneuvers as part of normal system operations, where ground personnel may employ mission planning and scheduling algorithms utilizing shortest-time maneuvers to determine the highest valued sequence of imaging or other spacecraft operations for a given activity window. Before commanding the satellite, a detailed check of all system constraints is also conducted to verify the mission plan and to ensure that all relevant hardware and operational constraints have been met. Such preflight checks may also include simulating the spacecraft attitude control system to verify that the spacecraft will behave as expected and remain within safe limits when the planned maneuvers are executed on orbit.
CMG momentum control systems create a unique challenge for controlling the attitude of a spacecraft. In particular, unlike an array of reaction wheels, whose torque capability is fixed with respect to the vehicle frame, the torque capability of a CMG array varies continuously with the gimbal angles. Consequently, ensuring accurate torque production on the spacecraft body requires proper configuration of the CMGs relative to one another, for example, to avoid gimbal configurations that result in singular states wherein torque cannot be produced in a certain direction. CMGs also have gimbal rate and input torque constraints that can be violated during the operation of the spacecraft, particularly if the spacecraft angular rates exceed predetermined limits, potentially leading to a loss of control of the spacecraft. Because of these complexities, devising a mechanism to ensure the predictability of shortest-time and other desired reorientations or maneuvers is an important aspect of the maneuver design problem for CMG spacecraft. Accordingly improved methods and apparatus are needed for determining and implementing spacecraft maneuvers while maintaining operation within torque and other physical or operational limits.